The problem is probably connected to this:
Bluetooth 4.0 in iOS 6 uses AVRCP1.4. Before this, it was AVRCP1.3. And a few months ago, the Bluetooth SIG certified AVRCP1.5.
So... somehow the backward compatibility broke between 1.4 and 1.3 devices. There are several ways this could happen - it could be Apple's fault entirely, or it could be the stereo manufacturer's fault, or both. The bug showed up with the iOS 6 update, so it's clearly connected to that.
Some stereos are working fine, others partly, others not at all. I suspect that the stereos (read: Pioneer, for example) are using firmware which fails to work with anything newer than 1.3. Pioneer's response has literally been that "everyone uses 1.3, Apple just changed to 1.4, and we only just found out about it" - but iOS 6 betas have been out for months. And it ignores the fact that version 1.5 was ratified months ago too.
Other manufacturers' stereos work fine (like a lot of Kenwoods or JVCs). Even a few Pioneers work fine. This is all listed on the manufacturer websites.
Pioneer has already listed the stereos they plan to update, but they give no other details (like dates).
Bottom line - it's not a simple issue from the user standpoint, and the fix may have to come from Apple, but I suspect it's more likely that the fix will come in form of stereo firmware updates. This has happened before, where an update from Apple, which used the standards correctly, uncovered a flaw in the 3rd party approach (which was subsequently fixed). Some people have speculated that the stereos relying on Parrot for bluetooth connectivity are the ones having problems (which is used by several brands).
Frustrating, and none of it makes it any easier for anyone to deal with.